How to make wall faces for this object?
if i understand correctly, you want this mesh on one side of a box shaped mesh? if so, you should extrude those edges over the Z-axis, then scale the resulting edges 
 to 0 over the Z-axis, and make a face on those edges.
shortcut to extrude over Z-axis: E->Z, followed by a value, or move with the mouse.
then to scale : S-> Z-> 0 to make it flat.
then press F with those edges selected, which will make a face.
As you pointed out yourself, answering your own question, you could use checker deselect to select every other vertex, and dissolve them.